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About the solvability of matrix polynomial equations
Author(s) -
Netzer Tim,
Thom Andreas
Publication year - 2017
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms.12056
Subject(s) - mathematics , matrix polynomial , matrix (chemical analysis) , polynomial , polynomial matrix , mathematical analysis , pure mathematics , composite material , materials science
We study self‐adjoint matrix polynomial equations in a single variable and prove existence of self‐adjoint solutions under some assumptions on the leading form. Our main result is that any self‐adjoint matrix polynomial equation of odd degree with non‐degenerate leading form can be solved in self‐adjoint matrices. We also provide results about equations of even degree and equations in many variables.